Fractals and chaos books

M. Barnsley, Fractals Everywhere, Academic Press Inc., 1988. This is an excellent text book on fractals. This is probably the best book for learning about the math underpinning fractals. It is also a good source for new fractal types.

R. Devaney and L. Keen, eds., Chaos and Fractals: The Mathematics Behind the Computer Graphics, American Mathematical Society, Providence, RI, 1989. This book contains detailed mathematical descriptions of chaos, the Mandelbrot set, etc.

R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison- Wesley, 1989. This book introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas. It goes into great detail on the exact structure of the logistic equation and other 1-D maps. The book is fairly mathematical using calculus and topology.

R. Devaney, Measure Topology and Fractal Geometry. This book provides the math necessary for the study of fractal geometry. It includes the background material on metric topology and measure theory and also covers topological and fractal dimension, including the Hausdorff dimension.

K. Falconer, Fractal Geometry: Mathematical Foundations and Applications.

J. Gleick, Chaos: Making a New Science. This popular book covers the origins of chaos.

S. Levy, Artificial Life : A Report from the Frontier Where Computers Meet Biology This book takes off where Gleick left off. It looks at many of the same people and what they are doing post-Gleick.

B. Mandelbrot, The Fractal Geometry of Nature. This is the classic book that made fractals famous. In this book Mandelbrot attempts to show that reality is fractal-like. He also has pictures of many different fractals. This book, however, is hard to understand unless you already know fractals.

H. O. Peitgen and P. H. Richter, The Beauty of Fractals. Lots of neat pictures. There is also an appendix giving the coordinates and constants for the color plates and many of the other pictures.

H. Peitgen and D. Saupe, eds., The Science of Fractal Images. This book contains many color and black and white photographs, high level math, and several pseudocoded algorithms.

H. Peitgen, H. Juergens and D. Saupe, Fractals for the Classroom. These two volumes are aimed at advanced secondary school students (but are appropriate for others too), have lots of examples, explain the math well, and give BASIC programs.

H. Peitgen, H. Juergens and D. Saupe Chaos and Fractals: New Frontiers of Science.

C. Pickover, Computers, Pattern, Chaos, and Beauty: Graphics from an Unseen World. This book contains a bunch of interesting explorations of different fractals.

J. Pritchard, The Chaos Cookbook: A Practical Programming Guide. It contains type- in-and-go listings in BASIC and Pascal. It also eases you into some of the mathematics of fractals and chaos in the context of graphical experimentation. So it's more than just a type-and-see-pictures book, but rather a lab tutorial, especially good for those with a weak or rusty (or even non- existent) calculus background.

P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants. A very good book on L-systems, which can be used to model plants in a VERY realistic fashion (the book contains a lot of pictures).

M. Schroeder, Fractals, Chaos, and Power Laws: Minutes from an Infinite Paradise. This book contains a clearly written explanation of fractal geometry with lots of puns and word play.

I. Stewart, Does God Play Dice?: the Mathematics of Chaos. A popular exposition of chaos.

Out of print

M. Barnsley and L. Hurd, _Fractal Image Compression_, Jones and Bartlett, December, 1992. ISBN 0-86720-457-5. This book explores the science of the fractal transform in depth. The authors begin with a foundation in information theory and present the technical background for fractal image compression. In so doing, they explain the detailed workings of the fractal transform. Algorithms are illustrated using source code in C.

M. Barnsley and L. Anson, _The Fractal Transform_, Jones and Bartlett, April, 1993. ISBN 0-86720-218-1. This book is a sequel to _Fractals Everywhere_. Without assuming a great deal of technical knowledge, the authors explain the workings of the Fractal Transform (tm). The Fractal Transform is the compression tool for storing high-quality images in a minimal amount of space on a computer. Barnsley uses examples and algorithms to explain how to transform a stored pixel image into its fractal representation.

R. L. Devaney, _Chaos, Fractals, and Dynamics_, Addison-Wesley, 1990. ISBN 0-201-23288-X. This is a very readable book. It introduces chaos fractals and dynamics using a combination of hands-on computer experimentation and precalculus math. Numerous full-color and black and white images convey the beauty of these mathematical ideas.

J. Feder, _Fractals_, Plenum Press, New York, 1988. This book is recommended as an introduction. It introduces fractals from geometrical ideas, covers a wide variety of topics, and covers things such as time series and R/S analysis that aren't usually considered.

B. Hao, ed., _Chaos_, World Scientific, Singapore, 1984. This is an excellent collection of papers on chaos containing some of the most significant reports on chaos such as ``Deterministic Nonperiodic Flow'' by E.N.Lorenz.

Ken Shirriff: [email protected] This page: http://www.righto.com/books/fractal.html Copyright 1998 Ken Shirriff.

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